1 Introduction What Is the Control system Toolbox? MaTLAB has a rich collection of functions immediately useful to the control engineer or system theorist. Complex arithmetic, eigenvalues, root-findssat matrix inversion, and FFTs are just a few examples of MATLAB's importa numerical tools. More generally, MATLABs linear algebra, matrix computation, and numerical analysis capabilities provide a reliable foundation for control system engineering as well as many other disciplines. The Control System Toolbox builds on the foundations of matlAb to provide functions designed for control engineering. The Control System Toolbox is a collection of algorithms, written mostly as M-files, that implements common control system design, analysis, and modeling techniques. Convenient graphical user interfaces(GUIs)simplify typical control engineering tasks Control systems can be modeled as transfer functions, in zero-pole-gain, or state-space form, allowing you to use both classical and modern control techniques. You can manipulate both continuous-time and discrete-time ystems Conversions between various model representations are provided Time responses, frequency responses, and root loci can be computed and graphed. Other functions allow pole placement, optimal control, and estimation. Finally, the Control System Toolbox is open and extensible. You can create custom M-files to suit your particular application 1-21 Introduction 1-2 What Is the Control System Toolbox? MATLAB® has a rich collection of functions immediately useful to the control engineer or system theorist. Complex arithmetic, eigenvalues, root-finding, matrix inversion, and FFTs are just a few examples of MATLAB’s important numerical tools. More generally, MATLAB’s linear algebra, matrix computation, and numerical analysis capabilities provide a reliable foundation for control system engineering as well as many other disciplines. The Control System Toolbox builds on the foundations of MATLAB to provide functions designed for control engineering. The Control System Toolbox is a collection of algorithms, written mostly as M-files, that implements common control system design, analysis, and modeling techniques. Convenient graphical user interfaces (GUI’s) simplify typical control engineering tasks. Control systems can be modeled as transfer functions, in zero-pole-gain, or state-space form, allowing you to use both classical and modern control techniques. You can manipulate both continuous-time and discrete-time systems. Conversions between various model representations are provided. Time responses, frequency responses, and root loci can be computed and graphed. Other functions allow pole placement, optimal control, and estimation. Finally, the Control System Toolbox is open and extensible. You can create custom M-files to suit your particular application